Subgroups — C₂×C₁₁×#2143 #14610577

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2143	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₁×#359	C₂	1	4	yes	maximal, complemented
6	C₂²×C₁₁×#41	—	2	1	no	—
7	C₂×C₁₁×#135	—	2	2	no	—
8	C₂×C₁₁×#135	—	2	1	no	—
9	C₂×C₁₁×#135	—	2	1	no	—
10	C₂×C₁₁×#135	—	2	2	no	—
11	C₂×C₁₁×#135	C₄	1	2	yes	—
12	C₂×C₁₁×#135	C₄	1	4	yes	—
13	C₂×C₁₁×#135	C₂²	1	2	yes	—
14	C₂×C₁₁×#135	C₂²	1	4	yes	—
15	C₂²×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
16	C₂²×C₁₁×SD₁₆	—	2	1	no	—
17	C₂²×C₁₁×D₈	C₄	1	1	yes	characteristic
18	C₂²×C₁₁×M₁₆	—	2	1	no	—
19	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×M₃₂	—	2	1	no	—
21	C₂×C₁₁×M₃₂	—	2	1	no	—
22	C₂×C₁₁×M₃₂	—	2	2	no	—
23	C₂×C₁₁×M₃₂	C₂²	1	4	yes	complemented
24	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	complemented
25	C₂×C₁₁×#108	—	2	2	no	—
26	C₂×C₁₁×#108	—	2	1	no	—
27	C₂×C₁₁×#108	C₂²	1	2	yes	complemented
28	C₂×C₁₁×#108	C₂²	1	4	yes	complemented
29	C₁₁×#359	C₂²	1	16	yes	complemented
30	C₂×C₁₁×#41	—	2	2	no	—
31	C₂×C₁₁×#41	—	2	4	no	—
32	C₂×C₁₁×#41	—	2	4	no	—
33	C₂×C₁₁×#41	—	2	2	no	—
34	C₂×C₁₁×#41	—	4	2	no	—
35	C₂×C₁₁×#41	—	4	1	no	—
36	C₂×C₁₁×#41	—	4	1	no	—
37	C₂×C₁₁×#41	—	4	2	no	—
38	C₂²×Q₈×C₁₁	—	2	1	no	—
39	C₂²×D₄×C₁₁	—	2	1	no	—
40	C₂²×D₄×C₁₁	—	4	1	no	—
41	C₂³×C₄×C₁₁	—	4	1	no	—
42	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
43	C₁₁×#135	—	2	4	no	—
44	C₁₁×#135	—	2	4	no	—
45	C₁₁×#135	—	2	4	no	—
46	C₁₁×#135	—	2	2	no	—
47	C₁₁×#135	—	2	4	no	—
48	C₁₁×#135	—	2	2	no	—
49	C₁₁×#135	—	2	4	no	—
50	C₁₁×#135	C₂×C₄	1	4	yes	—
51	C₁₁×#135	C₂×C₄	1	8	yes	—
52	C₁₁×#135	C₂³	1	4	yes	—
53	C₂×C₁₁×Q₁₆	—	2	2	no	—
54	C₂×C₁₁×Q₁₆	—	2	1	no	—
55	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
57	C₂×C₁₁×SD₁₆	—	2	4	no	—
58	C₂×C₁₁×SD₁₆	—	2	2	no	—
59	C₂×C₁₁×SD₁₆	—	2	2	no	—
60	C₂×C₁₁×SD₁₆	—	2	4	no	—
61	C₂×C₁₁×D₈	—	2	2	no	—
62	C₂×C₁₁×D₈	—	2	1	no	—
63	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
64	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
65	C₂×C₁₁×M₁₆	—	2	4	no	—
66	C₂×C₁₁×M₁₆	—	2	2	no	—
67	C₂×C₁₁×M₁₆	—	4	2	no	—
68	C₂×C₁₁×M₁₆	—	4	1	no	—
69	C₂²×C₈×C₁₁	—	4	1	no	—
70	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₁₁	D₄	1	2	yes	—
74	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₁	D₄	1	2	yes	—
78	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
80	C₁₁×M₃₂	—	2	4	no	—
81	C₁₁×M₃₂	—	2	4	no	—
82	C₂×C₁₁×C₁₆	—	2	2	no	—
83	C₂×C₁₁×C₁₆	—	2	2	no	—
84	C₂×C₁₁×C₁₆	C₂³	1	4	yes	complemented
85	C₁₁×#108	—	2	2	no	—
86	C₁₁×#108	—	2	4	no	—
87	C₁₁×#108	C₂³	1	4	yes	complemented
88	C₂×#2143	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₁	—	4	1	no	—
90	C₂⁴×C₁₁	SD₁₆	1	1	yes	characteristic
91	C₁₁×#41	—	2	8	no	—
92	C₁₁×#41	—	2	4	no	—
93	C₁₁×#41	—	2	4	no	—
94	C₁₁×#41	—	4	4	no	—
95	C₁₁×#41	—	4	4	no	—
96	C₁₁×#41	—	4	4	no	—
97	C₁₁×#41	—	4	4	no	—
98	C₁₁×#41	—	4	2	no	—
99	C₁₁×#41	—	4	4	no	—
100	C₁₁×#41	—	4	2	no	—
101	C₂×Q₈×C₁₁	—	2	4	no	—
102	C₂×Q₈×C₁₁	—	2	2	no	—
103	C₂×Q₈×C₁₁	—	4	2	no	—
104	C₂×Q₈×C₁₁	—	4	1	no	—
105	C₂×D₄×C₁₁	—	2	4	no	—
106	C₂×D₄×C₁₁	—	2	2	no	—
107	C₂×D₄×C₁₁	—	4	2	no	—
108	C₂×D₄×C₁₁	—	4	4	no	—
109	C₂×D₄×C₁₁	—	4	2	no	—
110	C₂×D₄×C₁₁	—	4	4	no	—
111	C₂×D₄×C₁₁	—	4	2	no	—
112	C₂×D₄×C₁₁	—	4	1	no	—
113	C₂²×C₄×C₁₁	—	4	1	no	—
114	C₂²×C₄×C₁₁	—	4	4	no	—
115	C₂²×C₄×C₁₁	—	4	2	no	—
116	C₂²×C₄×C₁₁	—	4	4	no	—
117	C₂²×C₄×C₁₁	—	4	2	no	—
118	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
121	C₂²×C₄×C₁₁	D₈	1	2	yes	—
122	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
128	C₁₁×Q₁₆	—	2	2	no	—
129	C₁₁×Q₁₆	—	2	4	no	—
130	C₁₁×Q₁₆	C₂²×C₄	1	4	yes	—
131	C₁₁×SD₁₆	—	2	4	no	—
132	C₁₁×SD₁₆	—	2	8	no	—
133	C₁₁×SD₁₆	—	2	4	no	—
134	C₁₁×D₈	—	2	2	no	—
135	C₁₁×D₈	—	2	4	no	—
136	C₁₁×D₈	C₂²×C₄	1	4	yes	—
137	C₁₁×M₁₆	—	2	4	no	—
138	C₁₁×M₁₆	—	4	4	no	—
139	C₁₁×M₁₆	—	4	2	no	—
140	C₂×C₈×C₁₁	—	4	4	no	—
141	C₂×C₈×C₁₁	—	4	2	no	—
142	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
143	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
145	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
147	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
148	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
149	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
160	C₁₁×C₁₆	—	2	4	no	—
161	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic
162	C₂²×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
163	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
164	#2143	C₂×C₁₁	1	8	yes	direct product factor
165	C₂×#359	C₂×C₁₁	1	4	yes	complemented
166	C₂³×C₁₁	—	4	2	no	—
167	C₂³×C₁₁	—	4	4	no	—
168	C₂³×C₁₁	—	4	2	no	—
169	C₂³×C₁₁	—	8	4	no	—
170	C₂³×C₁₁	#102	1	1	yes	characteristic
171	C₂³×C₁₁	#102	1	1	yes	characteristic
172	C₂³×C₁₁	#102	1	2	yes	—
173	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
174	C₂³×C₁₁	C₂×SD₁₆	1	2	yes	—
175	Q₈×C₁₁	—	2	4	no	—
176	Q₈×C₁₁	—	4	4	no	—
177	Q₈×C₁₁	—	4	2	no	—
178	D₄×C₁₁	—	2	4	no	—
179	D₄×C₁₁	—	4	4	no	—
180	D₄×C₁₁	—	4	8	no	—
181	D₄×C₁₁	—	4	4	no	—
182	D₄×C₁₁	—	4	4	no	—
183	D₄×C₁₁	—	4	2	no	—
184	C₂×C₄×C₁₁	—	4	4	no	—
185	C₂×C₄×C₁₁	—	4	2	no	—
186	C₂×C₄×C₁₁	—	4	4	no	—
187	C₂×C₄×C₁₁	—	4	8	no	—
188	C₂×C₄×C₁₁	—	4	4	no	—
189	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
190	C₂×C₄×C₁₁	#102	1	2	yes	—
191	C₂×C₄×C₁₁	#102	1	2	yes	—
192	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
193	C₂×C₄×C₁₁	#102	1	2	yes	—
194	C₂×C₄×C₁₁	#102	1	2	yes	—
195	C₂×C₄×C₁₁	#102	1	2	yes	—
196	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
201	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
202	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
203	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
205	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
207	C₈×C₁₁	—	4	4	no	—
208	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
210	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
212	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
213	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
214	C₂²×#41	—	2	1	no	—
215	C₂×#135	—	2	2	no	—
216	C₂×#135	—	2	1	no	—
217	C₂×#135	—	2	1	no	—
218	C₂×#135	—	2	2	no	—
219	C₂×#135	C₄×C₁₁	1	2	yes	—
220	C₂×#135	C₄×C₁₁	1	4	yes	—
221	C₂×#135	C₂²×C₁₁	1	2	yes	—
222	C₂×#135	C₂²×C₁₁	1	4	yes	—
223	C₂²×Q₁₆	C₄×C₁₁	1	1	yes	characteristic
224	C₂²×SD₁₆	—	2	1	no	—
225	C₂²×D₈	C₄×C₁₁	1	1	yes	characteristic
226	C₂²×M₁₆	—	2	1	no	—
227	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
228	C₂×M₃₂	—	2	1	no	—
229	C₂×M₃₂	—	2	1	no	—
230	C₂×M₃₂	—	2	2	no	—
231	C₂×M₃₂	C₂²×C₁₁	1	4	yes	complemented
232	C₂²×C₁₆	C₂²×C₁₁	1	2	yes	complemented
233	C₂×#108	—	2	2	no	—
234	C₂×#108	—	2	1	no	—
235	C₂×#108	C₂²×C₁₁	1	2	yes	complemented
236	C₂×#108	C₂²×C₁₁	1	4	yes	complemented
237	#359	C₂²×C₁₁	1	16	yes	complemented
238	C₂²×C₁₁	—	2	2	no	—
239	C₂²×C₁₁	—	2	2	no	—
240	C₂²×C₁₁	—	2	2	no	—
241	C₂²×C₁₁	—	4	2	no	—
242	C₂²×C₁₁	—	4	2	no	—
243	C₂²×C₁₁	—	4	4	no	—
244	C₂²×C₁₁	—	8	8	no	—
245	C₂²×C₁₁	—	8	4	no	—
246	C₂²×C₁₁	C₂×#102	1	2	yes	—
247	C₂²×C₁₁	C₂×#102	1	2	yes	—
248	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
249	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
250	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
251	C₄×C₁₁	—	4	4	no	—
252	C₄×C₁₁	C₂×#102	1	2	yes	—
253	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
254	C₄×C₁₁	C₂×#102	1	2	yes	—
255	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
256	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
257	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	4	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	4	no	—
262	C₂×#41	—	4	1	no	—
263	C₂×#41	—	4	2	no	—
264	C₂×#41	—	4	1	no	—
265	C₂×#41	—	4	2	no	—
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	4	1	no	—
269	C₂³×C₄	—	4	1	no	—
270	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
271	#135	—	2	4	no	—
272	#135	—	2	4	no	—
273	#135	—	2	4	no	—
274	#135	—	2	2	no	—
275	#135	—	2	4	no	—
276	#135	—	2	2	no	—
277	#135	—	2	4	no	—
278	#135	C₂×C₄×C₁₁	1	4	yes	—
279	#135	C₂×C₄×C₁₁	1	8	yes	—
280	#135	C₂³×C₁₁	1	4	yes	—
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	—	2	1	no	—
283	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
284	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
285	C₂×SD₁₆	—	2	4	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×SD₁₆	—	2	2	no	—
288	C₂×SD₁₆	—	2	4	no	—
289	C₂×D₈	—	2	2	no	—
290	C₂×D₈	—	2	1	no	—
291	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
292	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	4	no	—
295	C₂×M₁₆	—	4	1	no	—
296	C₂×M₁₆	—	4	2	no	—
297	C₂²×C₈	—	4	1	no	—
298	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
299	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
300	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
301	C₂²×C₈	D₄×C₁₁	1	2	yes	—
302	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
303	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
304	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
305	C₂²×C₈	D₄×C₁₁	1	2	yes	—
306	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
308	M₃₂	—	2	4	no	—
309	M₃₂	—	2	4	no	—
310	C₂×C₁₆	—	2	2	no	—
311	C₂×C₁₆	—	2	2	no	—
312	C₂×C₁₆	C₂³×C₁₁	1	4	yes	complemented
313	#108	—	2	2	no	—
314	#108	—	2	4	no	—
315	#108	C₂³×C₁₁	1	4	yes	complemented
316	C₂×C₁₁	—	2	2	no	—
317	C₂×C₁₁	—	2	1	no	—
318	C₂×C₁₁	—	2	2	no	—
319	C₂×C₁₁	—	2	1	no	—
320	C₂×C₁₁	—	8	4	no	—
321	C₂×C₁₁	#2143	1	2	yes	direct product factor
322	C₂×C₁₁	C₂²×#102	1	1	yes	characteristic
323	C₂⁴	—	4	1	no	—
324	C₂⁴	C₁₁×SD₁₆	1	1	yes	characteristic
325	#41	—	2	4	no	—
326	#41	—	2	8	no	—
327	#41	—	2	4	no	—
328	#41	—	4	4	no	—
329	#41	—	4	4	no	—
330	#41	—	4	4	no	—
331	#41	—	4	4	no	—
332	#41	—	4	2	no	—
333	#41	—	4	2	no	—
334	#41	—	4	4	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	1	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
353	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
355	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
356	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
357	C₂²×C₄	C₁₁×D₈	1	2	yes	—
358	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
359	C₂²×C₄	C₁₁×SD₁₆	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
362	Q₁₆	—	2	2	no	—
363	Q₁₆	—	2	4	no	—
364	Q₁₆	C₂²×C₄×C₁₁	1	4	yes	—
365	SD₁₆	—	2	4	no	—
366	SD₁₆	—	2	8	no	—
367	SD₁₆	—	2	4	no	—
368	D₈	—	2	2	no	—
369	D₈	—	2	4	no	—
370	D₈	C₂²×C₄×C₁₁	1	4	yes	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	4	4	no	—
373	M₁₆	—	4	2	no	—
374	C₂×C₈	—	4	4	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
377	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
378	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
379	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
380	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
381	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
382	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
383	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
384	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
385	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
386	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
387	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
388	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
391	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
392	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
393	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
394	C₁₆	—	2	4	no	—
395	C₁₁	C₂×#2143	1	1	yes	characteristic, direct product factor, Sylow
396	C₂³	—	4	2	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	8	4	no	—
400	C₂³	C₁₁×#102	1	1	yes	characteristic
401	C₂³	C₁₁×#102	1	1	yes	characteristic
402	C₂³	C₁₁×#102	1	2	yes	—
403	C₂³	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
404	C₂³	C₂×C₁₁×SD₁₆	1	2	yes	—
405	Q₈	—	2	4	no	—
406	Q₈	—	4	4	no	—
407	Q₈	—	4	2	no	—
408	D₄	—	2	4	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	C₁₁×#102	1	2	yes	—
420	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
421	C₂×C₄	C₁₁×#102	1	2	yes	—
422	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
423	C₂×C₄	C₁₁×#102	1	2	yes	—
424	C₂×C₄	C₁₁×#102	1	2	yes	—
425	C₂×C₄	C₁₁×#102	1	2	yes	—
426	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
427	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
428	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
429	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
430	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
431	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
432	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
435	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
437	C₈	—	4	4	no	—
438	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
439	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
440	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
441	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
442	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
443	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	8	no	—
451	C₂²	—	8	4	no	—
452	C₂²	C₂×C₁₁×#102	1	2	yes	—
453	C₂²	C₂×C₁₁×#102	1	2	yes	—
454	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
455	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
456	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
457	C₄	—	4	4	no	—
458	C₄	C₂×C₁₁×#102	1	2	yes	—
459	C₄	C₂×C₁₁×#102	1	1	yes	characteristic
460	C₄	C₂×C₁₁×#102	1	2	yes	—
461	C₄	C₂×C₁₁×#102	1	1	yes	characteristic
462	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
463	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	2	2	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	8	4	no	—
469	C₂	C₁₁×#2143	1	2	yes	direct product factor
470	C₂	C₂²×C₁₁×#102	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₈
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×#102
prime radical	C₂²×C₁₁×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×C₁₁×M₃₂	C₂	semidirect
3. C₂²×C₁₁×#108	C₂	semidirect
4. C₁₁×#2143	C₂	direct (N × H)
5. C₂×C₁₁×#359	C₂	semidirect
23. C₂×C₁₁×M₃₂	C₂²	semidirect
24. C₂²×C₁₁×C₁₆	C₂²	semidirect
27. C₂×C₁₁×#108	C₂²	semidirect
28. C₂×C₁₁×#108	C₂²	semidirect
29. C₁₁×#359	C₂²	semidirect
84. C₂×C₁₁×C₁₆	C₂³	semidirect
87. C₁₁×#108	C₂³	semidirect
88. C₂×#2143	C₁₁	direct (N × H)
162. C₂²×M₃₂	C₂×C₁₁	semidirect
163. C₂²×#108	C₂×C₁₁	semidirect
164. #2143	C₂×C₁₁	direct (N × H)
165. C₂×#359	C₂×C₁₁	semidirect
231. C₂×M₃₂	C₂²×C₁₁	semidirect
232. C₂²×C₁₆	C₂²×C₁₁	semidirect
235. C₂×#108	C₂²×C₁₁	semidirect
236. C₂×#108	C₂²×C₁₁	semidirect
237. #359	C₂²×C₁₁	semidirect
312. C₂×C₁₆	C₂³×C₁₁	semidirect
315. #108	C₂³×C₁₁	semidirect
321. C₂×C₁₁	#2143	direct (N × H)
395. C₁₁	C₂×#2143	direct (N × H)
469. C₂	C₁₁×#2143	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₁×#135	2
C₂²×C₁₁×M₃₂	2
C₂²×C₁₁×#108	2
C₁₁×#2143	2
C₂×C₁₁×#359	2
C₂×#2143	11

Subgroups — C2×C11×#2143 #14610577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2143 #14610577